[en] The calculation of three-dimensional magnetohydrodynamic (MHD) toroidal plasma equilibria is a challenging one conceptually because of the problems of Hamiltonian field-line chaos and singular currents. Combined with the need to achieve high accuracy for plasma stability calculations, this makes the problem very difficult, but important for advanced fusion experiments. A new approach based on multiple relaxed regions separated by ideal-MHD toroidal barrier tori is presented. This is cast as a variational principle, with the second variation giving necessary stability conditions for both ideal MHD and resistive MHD (in the limit of small resistivity). (author)